Error correction of a predictive ocean wave model using local model approximation

Constructing models from time series with nontrivial dynamics is a difficult problem. The classical approach is to build a model from first principles and use it to forecast on the basis of the initial conditions. Unfortunately, this is not always possible. For example, in fluid dynamics, a perfect model in the form of the Navier-Stokes equations exists, but initial conditions and accurate forcing terms are difficult to obtain. In other cases, a good model may not exist. In either case, alternative approaches should be examined. This paper describes an alternative approach of combining observations and numerical model results in order to produce an accurate forecast. The approach is based on application of a method inspired by chaos theory for building nonlinear models from data called Local Models. Embedding theorem based on the time lagged embedded vectors is the basis for the local model. This technique is used for analysis and updating of numerical model output variables to forecast and correct the errors created by numerical model. The local model approximation is a powerful tool in the forecasting of chaotic time series and has been employed for wave prediction in a forecasting horizon from a few hours to 24 h. The efficacy of the local model as an error correction tool (by combining the model predictions with the observations) compared with the predictions of linear auto regressive models has been brought up. In the present study, the parameters driving the local model are optimized using evolutionary algorithms.